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Electron doping is an excellent tuning knob to explore different phases ofmatter in two-dimensional (2D) materials. For example, tuning the Fermi levelat a van Hove singularity in twisted bilayer graphene can enhanceelectron-electron interactions and induce a diverse range of correlated phases.Here, using a single-particle picture, we study the electronic reconstructionof the band edges of a 2D semiconductor, monolayer MoS2, on a hexagonal moirepotential induced by another MoS2 monolayer. We find that such systemtransitions from a honeycomb to a hexagonal symmetry when the Fermi level istuned from the conduction to the valence side. We also study the system undermagnetic fields, and construct the Hofstadter's butterfly in the electron- andhole-doped side. Our findings are confirmed by simulating the conductanceacross a large-scale two-terminal device. We conclude that this duality is ageneral property that MoS2 and other transition-metal-dichalcogenides exhibitunder non-symmetric superlattice potentials.

Fractal Quantum Transport on MoS2 Superlattices: a System with Tunable Symmetry